Quantum mechanics began as a desperate measure to get around some spectacular failures of what subsequently came to be known as classical physics.

In 1900 Max Planck discovered a law that perfectly describes the spectrum of a glowing hot object. Planck's radiation formula turned out to be irreconcilable with the physics of his time. (If classical physics were right, you would be blinded by ultraviolet light if you looked at the burner of a stove, aka the UV catastrophe.) At first, it was just a fit to the data, "a fortuitous guess at an interpolation formula" as Planck himself called it. Only weeks later did it turn out to imply the quantization of energy for the emission of electromagnetic radiation: the energy of a quantum of radiation is proportional to the frequency of the radiation, the constant of proportionality being Planck's constant

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We can of course use the angular frequency instead of . Introducing the reduced Planck constant , we then have

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This theory is valid at all temperatures and helpful in explaining radiation by black bodies.

In 1911 Ernest Rutherford proposed a model of the atom based on experiments by Geiger and Marsden. Geiger and Marsden had directed a beam of alpha particles at a thin gold foil. Most of the particles passed the foil more or less as expected, but about one in 8000 bounced back as if it had encountered a much heavier object. In Rutherford's own words this was as incredible as if you fired a 15 inch cannon ball at a piece of tissue paper and it came back and hit you. After analysing the data collected by Geiger and Marsden, Rutherford concluded that the diameter of the atomic nucleus (which contains over 99.9% of the atom's mass) was less than 0.01% of the diameter of the entire atom. He suggested that the atom is spherical in shape and the atomic electrons orbit the nucleus much like planets orbit a star.He calculated mass of electron as 1/7000th part of mass of alpha particle.Rutherford's atomic model is also called the Nuclear model.

The problem of having electrons orbit the nucleus the same way that a planet orbits a star is that classical electromagnetic theory demands that an orbiting electron will radiate away its energy and spiral into the nucleus in about 0.5×10-10 seconds. This was the worst quantitative failure in the history of physics, under-predicting the lifetime of hydrogen by at least forty orders of magnitude! (This figure is based on the experimentally established lower bound on the proton's lifetime.)